Convergence Analysis of River Formation Dynamics Algorithm

Abstract

As many real-life optimization problems are difficult to solve by exact optimization methods, a number of metaheuristics are developed over the years to search for viable solutions, e.g., river formation dynamics (RFD) algorithm. RFD algorithm is based on the analogy that water drops traverse from source to destination by following a random probabilistic search strategy. This search strategy is employed to solve various optimization problems in practice. However, the search strategy of RFD algorithm lacks theoretical analysis and the convergence property of RFD algorithm needs mathematical reasoning for comprehensive understanding of the working mechanism. In this paper, the random search strategy of RFD algorithm is analyzed mathematically and the convergence property of the algorithm is examined by using Markov chain theory. Several conditions for convergence are showcased and it is proved that RFD algorithm can indeed satisfy these conditions to achieve global optimality efficiently. Further, several experiments are performed on a set of single objective test functions to demonstrate the convergence of RFD algorithm in practice.